We consider the weak convergence of the Euler-Maruyama approximation for Schr\"odinger-F\"ollmer diffusions, which are solutions of Schr\"odinger bridge problems and can be used for sampling from given distributions. We show that the distribution of the terminal random variable of the time-discretized process weakly converges to the target one under mild regularity conditions.

翻译：我们研究薛定谔-弗尔默扩散的欧拉-丸山逼近的弱收敛性。此类扩散是薛定谔桥问题的解，可用于从给定分布中进行采样。我们证明，在温和的正则条件下，时间离散化过程末端随机变量的分布弱收敛于目标分布。